Traffic Jam X05864

Luke and Lucy are caught in a traffic jam, and they are bored, so they create a new game to play. The board is a street divided into small cells, numbered from 1. Some cars are standing on the street.

Lucy plays first, and in each turn, a player can take one car and moves it toward 1. A car cannot stand in a place where another car already is, and cannot jump over other cars. The player who makes the last move (after which cars are standing in positions 1, 2, …, N) wins.

Who will win the game, assuming that both players play optimally?

Input

The first line of input contains a single integer N, the number of cars (1 ≤ N ≤ 10000).

For i = 1 to N, i-th following line contains a_i, the number of the cell where i-th car is standing, 1 ≤ a₁ ≤ a₂ ⋯ a_N ≤ 100000000.

Output

Output either Lucy or Luke.